Optical arrangement, method of use, and method for determining a diffraction grating

Abstract

An optical arrangement includes a light source which emits coherent light of a wavelength λ, and a diffraction grating which has a multiplicity of diffraction structures which follow one another periodically at the spacing of a grating period d and are arranged along a base surface, the individual diffraction structures respectively having a blaze flank and an antiblaze flank, the blaze flanks being arranged at an angle β and the antiblaze flanks being arranged at an angle α to the base surface, and respectively neighbouring blaze and antiblaze flanks enclosing an apex angle γ, and an incident light beam being arranged at a Littrow angle θ L relative to a grating normal of the diffraction grating. The angle β of the blaze flanks to the base surface is selected as a function of the Littrow angle θ L such that the diffraction efficiency is at least approximately maximal in one of the largest diffraction orders m, which still fulfils the condition (2((m+1)/m)−1)sin θ L ≧1, and for at least one polarization direction.

What is claimed is: 
     
       1. An optical arrangement, comprising:
 a diffraction grating comprising a plurality of diffraction structures following one another periodically at a spacing of a grating period (d); and 
 a base having a base surface supporting the plurality of diffraction structures, 
 wherein each of the plurality of diffraction structures comprises: 
 a blaze flank; and
 an antiblaze flank, the blaze flanks being arranged at an angle (β) relative to the base surface, the antiblaze flanks being arranged at an angle (α) relative to the base surface, and neighbouring blaze and antiblaze flanks enclosing an apex angle (γ), and 
 
 wherein, during use:
 the optical arrangement is configured so that an incident light beam at a wavelength (λ) is arranged at a Littrow angle (θ L ) relative to a grating normal of the diffraction grating; 
 the angle (β) is greater than the Littrow angle (θ L ) by at least 4°; 
 for at least one polarization direction, a diffraction efficiency is at least approximately maximal in a diffraction order m, which fulfils the condition (2((m+1)/m)−1)sin θ L ≧1; and 
 the diffraction order m is a largest possible last propagating diffraction order or the diffraction order m deviates from the largest possible last propagating diffraction order by a number which lies in a range from 1 to 20. 
 
 
     
     
       2. The optical arrangement of  claim 1 , wherein the angle (β) is greater than the Littrow angle (θ L ) by a value in a range from 4° to 10°. 
     
     
       3. The optical arrangement of  claim 1 , wherein the angle (β) is greater than the Littrow angle (θ L ) by a value in a range from 4° to 8°. 
     
     
       4. The optical arrangement of  claim 1 , wherein each diffraction efficiency of two polarizations is at least approximately maximal in the diffraction order m. 
     
     
       5. The optical arrangement of  claim 1 , wherein the apex angle (γ) is in a range from 88.5° to 91.5°. 
     
     
       6. The optical arrangement of  claim 1 , wherein the angle (β) is in a range from 82° to 86°, and the Littrow angle (θ L ) is in a range from 78° to 80°. 
     
     
       7. The optical arrangement of  claim 1 , wherein, during use, the diffraction grating is inclined by an inclination angle (δ) relative to an incidence plane of the light beam. 
     
     
       8. The optical arrangement of  claim 7 , wherein the inclination angle (δ) is in a range from 35° to near 90°. 
     
     
       9. The optical arrangement of  claim 1 , wherein the diffraction order m is the largest possible last propagating diffraction order. 
     
     
       10. The optical arrangement of  claim 1 , wherein the diffraction order m deviates from the largest possible last propagating diffraction order by a number which lies in a range from 1 to 20. 
     
     
       11. The optical arrangement of  claim 1 , wherein the diffraction order m deviates from the largest possible last propagating diffraction order by a number which lies in a range from 1 to 10. 
     
     
       12. The optical arrangement of  claim 1 , further comprising a light source configured to emit coherent light at the wavelength (λ). 
     
     
       13. A method, comprising:
 providing the optical arrangement of  claim 1 ; and 
 using the diffraction grating as an end mirror of a laser resonator. 
 
     
     
       14. A method, comprising:
 selecting a Littrow angle (θ L ) at which coherent light of a wavelength (λ) is to be incident on a diffraction grating relative to a grating normal of the diffraction grating; 
 selecting a diffraction order m which satisfies the condition (2((m+1)/m)−1)sin θ L ≧1, where the diffraction order m is a largest possible last propagating diffraction order for the Littrow angle (θ L ) or the diffraction order m deviates from the largest possible last propagating diffraction order for the Littrow angle (θ L ) by a number which lies in a range from 1 to 20; 
 determining a grating period d of the diffraction grating in accordance with the equation: d=mλ/(2sin θ L ); 
 selecting an angle (β) as a function of the diffraction order m and the grating period d from an angular range in which a diffraction efficiency in the diffraction order m is at least approximately maximal; and 
 providing the diffraction grating which comprises a plurality of diffraction structures following one another periodically at a spacing of the grating period (d) and arranged along a base surface, each diffraction structure comprising a blaze flank arranged at the angle (β) relative to the base surface. 
 
     
     
       15. The method of  claim 14 , wherein the diffraction order m is determined as the largest possible last propagating diffraction order L in accordance with the equation:
     L =max m≧1, mεN {(2(( m+ 1)/ m )−1)sin θ L≧ 1}.
 
 
     
     
       16. The method of  claim 14 , wherein the diffraction order m is deviates from the largest possible last propagating diffraction order L by a number which is in a range from 1to 20. 
     
     
       17. The method of  claim 14 , wherein the angle (β) is selected so that each diffraction efficiency of two polarization directions is at least approximately maximal in the diffraction order m. 
     
     
       18. The method of  claim 14 , wherein the apex angle (λ) is from 88.5° to 91.5°. 
     
     
       19. The method of  claim 14 , wherein the grating period (d) is determined in accordance with the equation: d=mλ/(2sin θ L  cos δ), δbeing an inclination angle at which the diffraction grating is inclined to the incidence plane of the light beam. 
     
     
       20. The method of  claim 14 , wherein the angle (β) is greater than the Littrow angle (θ L ) by at least 4°. 
     
     
       21. The method of  claim 14 , wherein the angle (β) is greater than the Littrow angle (θ L ) by a value in a range from 4° to 8°. 
     
     
       22. The method of  claim 14 , wherein the angle (β) is greater than the Littrow angle (θ L ) by a value in a range from 4° to 10°.